CHAP. IV. THE elements for a solar eclipse are computed in the same manner as the elements of a lunar eclipse; all of which are General difound by the solar and lunar tables. The approximate time of new moon is first computed, and for this time, compute the sun's longitude, declination, parallax, semidiameter, and hourly motion; and for the same time compute the moon's longitude, latitude, hourly motion in longitude and latitude, horizontal parallax, and semidiameter. to rections ments. If the longitudes of both sun and moon are found to be the same, then the approximate time of conjunction; found by the lunation tables, is the same as the true time; if not, we proportion to the true time, as described in the last chapter. The elements for a general solar eclipse are: 1. The time of dat some known meridian. 2. Longi- What ele tude of and 3. O's declination. 4. 's latitude. 5. O's hourly motion. 6. 's hourly motion in longitude. 7. O's hourly motion in latitude. 8. The angle of the 's visible path with the ecliptic. 9. O's horizontal parallax. 10. O's semidiameter. 11. O's semidiameter. 12. O's horizontal parallax. For a local eclipse, the latitude of the particular locality must also be given, or considered as one of the elements. As we can best illustrate general principles by taking a particular example, we now propose to show the general course of an eclipse of the sun, which will occur in May 1854; where it will first commence on the earth; in what latitude and longitude the sun will be centrally eclipsed at noon, and where; in what latitude and longitude the eclipse will finally leave the earth. ments are necessary. A definite example pro posed. We speak of an eclipse of the sun being on the earth; by Some general prelimi this we mean the moon's shadow on the earth. If an observer nary expla is in the moon's shadow, of course, the sun would be in an nations. eclipse to him; and, if a tangent line be drawn between the *Sign of conjunction. CHAP. IV. sun and moon, and that line strike the eye of an observer on the earth, to that observer the limbs of the sun and moon would apparently meet, and all projections of eclipses are on the principle of lines drawn from some part of the sun to some part of the moon, and those lines striking the earth. When no such lines can strike the earth there can be no eclipse. For the sake of simplicity in explaining a projection of a solar eclipse, whether it be general or local, an observer is supposed to be at the moon, looking down on the earth, viewing the moon's shadow as it passes over the earth's disc; and, of course, the earth to him appears as a plane, equal to the moon's horizontal parallax. Point of view. Accurate elements for the solar eclipse, which will The approximate time of new moon will be found computed on page 254, and, if very close results are not required, we may compute the sun's longitude, declination, hourly motion, and semidiameter for this time, and take out the moon's horizontal parallax, hourly motion, and semidiameter from Table IX; but we have computed the elements more accurately by the lunar tables, and find them as follows: d. h. m. S. 1. Greenwich mean time of 1854, May 26 8 45 39 2. Lon. of and 3. Declination of the 4. Latitude of the 5. O's hourly motion in lon., take place May 26, 1854. 65° 14' 6" 21 11 43 N. 21 19 N. 2 24 's hourly motion in lat., tending north, From 5, 6, and 7 we obtain 8, as explained 5 42 50 54 30 14 51 15 48 9 12. The O's horizontal parallax, always taken at 's hori Add together the O's horizontal parallax, the zontal parallax, and the semidiameters of and, and if the moon's latitude is less than this sum, there will be an eclipse, otherwise not; and it is by comparing this sum with CHAP. IV. the moon's latitude that all doubtful cases are decided. TO CONSTRUCT A GENERAL ECLIPSE. pre 1. Make, or procure, a convenient scale of equal parts, and from any point as C (Fig. 56) with the radius CB, equal to the difference of the parallaxes of and (in the sent example 54′ 21′′, the minute is the unit), describe the semicircle CB PH, or the whole circle, when the case requires it. When the moon has small latitude (less than 20') describe the whole circle; when the moon has large north latitude, describe the northern semicircle; when south, describe the southern semicircle. Through C draw VCD PL perpendicular to HB. This perpendicular will represent the plane of the earth's axis, as seen from the moon. From P take PA, PF, each equal to the obliquity of the ecliptic 23° 27' 30", and draw the chord A F. On AF, as a diameter, describe the semicircle ALF. How to find the axis tic. 2. Find the distance of the sun from the tropic, nearest to of the eclipit, by taking the difference between the sun's longitude and 90° or 270°, as the case may be. In the present example we subtract 65° 14′ from 90°, the remainder is 24° 46'. LT, equal to 24° 46', and draw TE parallel to LC. Draw CE the axis of the ecliptic. Take By the revolution of the earth round the sun, the axis of The axis of the eclipthe ecliptic appears to coincide with the axis of the equator, tic variable when the sun is at either tropic, and it appears to depart in position. from that line by the whole amount of the obliquity of the ecliptic; and the time of this greatest departure is when the sun is on the equator. That is, CE runs out to CA at the vernal equinox, and runs out to CF at the autumnal equinox. As a general rule, CE, the axis of the ecliptic, is to the left of CP, the axis of the equator, from the 20th of December to the 20th of June, and to the right of that line the rest of the year. Draw CG the axis of the moon's orbit, so How to find that the angle GCE shall be equal to the angle of the moon's visible path with the ecliptic, and CG is to the left of bit. ** the axis of the lunar or CHAP. IV. CE when the eclipse is about the ascending node, as in this example, but at the right when the eclipse is about the decending node. tor. The equa. How draw to moon's path. For this projection to appear natural, the reader should face the north, so that H will appear to the west, and B on the east of the figure. The shadow of the moon across the earth is from a western to an eastern direction, therefore, the moon is conceived to come in on the earth from the west side. The point C is perpendicular to the sun's declination, and CV is the sine of the declination, and the curved line HVB is a representation of the equator as seen from the moon. When the sun has no declination, the equator draws up into a straight line. 3. Take Cn from the scale of equal parts, making it equal the to the moon's latitude, and through the point n, and at right angles to CG, draw the line klmnrpq, which represents the center of the shadow, or the moon's path across the disc. How to de From C as a center, at the distance C O, describe the outer semicircle, equal to the sum of the moon's horizontal parallax, the sun's horizontal parallax, and the semidiameter of both sun and moon; then OH is the semidiameter of the sun and moon. When the eclipse first commences, the center of the moon is at k, and the center of the sun is on the circumference of the other circle, in a direct line to C, not represented in the figure, therefore, the two limbs must then just touch. As C is the center of the earth, and H on the equator, therefore CHO is a line in the plane of the equator, and the point k is a little below the equator; which shows that the eclipse first commences on the earth a little south of the equator. The time that the eclipse is on the earth is measured by termine the the time required for the moon to pass from k to q with its true angular motion from the sun. duration of a general eclipse. The length of this line, k q, can be found from the elements, and trigonometry, as in an eclipse of the moon, and the time of describing it is found in the same way. |